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Bilaniuk S. — A Problem Course in Mathematical Logic (vol. 2)

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Название: A Problem Course in Mathematical Logic (vol. 2)

Автор: Bilaniuk S.

Аннотация:

This is the Volume II of a text for a problem-oriented undergraduate course in mathematical logic. It covers the basics of computability, using Turing machines and recursive functions, and Goedel's Incompleteness Theorem, and could be used for a one semester course on these topics. Volume I, Propositional and First-Order Logic, covers the basics of these topics through the Soundness, Completeness, and Compactness Theorems. Information on availability and the conditions under which this book may be used and reproduced are given in the preface.

Язык:

Рубрика: Математика/Алгебра/Математическая логика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Version 1.3

Год издания: 1997

Количество страниц: 83

Добавлена в каталог: 09.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$f : \mathbb{N}^k \to \mathbb{N}$       25
$i_{\mathbb{N}}$       26
-place function      25
-place relation      25
-state entry in busy beaver competition      27
-state Turing machine      9
$P \cap Q$       32
$P \cup Q$       32
$P \vee Q$       32
$P \wedge Q$       32
$S^{m_0}$       50
$\alpha$       33
$\lceil \triangle \rceil$       46
$\mathbb{N}$       25
$\mathbb{N}k^$       25
$\mathbb{N}^k \textbackslash \mathcal{P}$       32
$\mathcal{A}$       49
$\mathcal{L_N}$       43
$\mathfrak{N}$       44
$\mathrm{A}$       33
$\mathrm{Code}_k$       70
$\mathrm{Comp}$       39
$\mathrm{Comp}_M$       38
$\mathrm{Conclusion}_{\triangle}$       46
$\mathrm{Con}(\sum)$       54
$\mathrm{Decode}$       70
$\mathrm{Deduction}_{\triangle}$       46
$\mathrm{Diff}$       27 31
$\mathrm{Div}$       33 52
$\mathrm{Element}$       33 52
$\mathrm{Entry}$       38
$\mathrm{Equal}$       33
$\mathrm{Exp}$       31
$\mathrm{Fact}$       31
$\mathrm{Formulas}$       46
$\mathrm{Formula}$       46
$\mathrm{Inference}$       46
$\mathrm{IsPrime}$       33 52
$\mathrm{Length}$       33 52
$\mathrm{Logical}$       46
$\mathrm{Mult}$       31
$\mathrm{O}$       27 29 51
$\mathrm{Power}$       33 52
$\mathrm{Pred}$       27 31
$\mathrm{Premiss}_{\triangle}$       46
$\mathrm{Prime}$       33 52
$\mathrm{Sentence}$       46
$\mathrm{Sim}$       39
$\mathrm{Subseq}$       33
$\mathrm{Sub}$       53
$\mathrm{Sum}$       27 30
$\mathrm{S}$       27 29 51
$\mathrm{TapePosSeq}$       69
$\mathrm{TapePos}$       69
$\mathrm{Term}$       46
$\mathrm{Th}(\mathfrak{N})$       54
$\mathrm{Th}(\sum)$       44
$\mathrm{TM}$       39
$\mathrm{TM}_M$       38
$\neg P$       32
$\pi^{k}_i$       29 51
$\varphi(S^{m_1} 0; ... ; S^{m_k} 0)$       50
Ackerman's Function      33
Alphabet      7 13
Blank, cell      7
Blank, tape      7
Bounded minimalization      36
Busy beaver competition      27
Busy beaver competition score      27
Busy beaver competition, -state entry      27
Cell blank      7
Cell marked      7
Cell scanned      8
Characteristic function      26
Church's thesis      2
Code      20
Code of a sequence of tape position      37
Code of tape position      37
Code of Turing machine      38
Code, sequence of tape positions      37
Code, tape position      37
Code, Turing machine      38
complete      2
Complete set of sentences      44
Completeness      44
Completeness theorem      1
composition      29
Computable function      26
Computable set of formulas      46
Computation      11
Computation, partial      11
Constant function      30
Decision problem      1
Definable function      55
Definable relation      55
Domain of a function      25

Entscheidungsproblem      1 43
First-order language for number theory      43
Fixed-Point Lemma      53
Function, -place      25
Function, bounded minimalization of      36
Function, composition of      29
Function, computable      26
Function, constant      30
Function, definable in $\mathfrak{N}$       55
Function, domain of      25
Function, identity      26
Function, initial      29
Function, partial      25
Function, primitive recursion of      30
Function, primitive recursive      31
Function, projection      29
Function, recursive      36
Function, regular      35
Function, successor      29
Function, Turing computable      26
Function, unbounded minimalization of      35
Function, zero      29
Goedel (First) Incompleteness Theorem      53
Goedel code sequences      45
Goedel Incompleteness Theorem      43
Goedel Second Incompleteness Theorem      54
Goedel symbols of $\mathcal{L}_N$       45
halt      11
Halting problem      17 22
Identity function      26
Iinput tape      11
Image of a function      25
Initial function      29
Language first-order number theory      43
machine      9
Marked cell      7
Minimalization bounded      36
Minimalization unbounded      35
Natural numbers      25
Number theory first-order language for      43
Output tape      11
Partial computation      11
Patial function      25
Pig, yellow      19
Position tape      8
Primitive recursion      30
Primitive recursive function      31
Primitive relation      32
Projection function      29
r.e.      39
Recursion, primitive      30
Recursive function      36
Recursive relation      36
Recursive set of formulas      46
Recursively enumerable      39
Recursively set of formulas      46
Regular function      35
Relation -place      25
Relation characteristic function      26
Relation definable in $\mathfrak{N}$       55
Relation, primitive recursive      32
Relation, Turing computable      36
Representable function      50
Representable relation      50
Representation of a tape position      19
Representation of a Turing machine      18
Representation of tape position      19
Representation of Turing machine      18
Scanned cell      8
Scanner      13
Score busy beaver competition      27
State      8 9
Successor function      29
Successor tape position      11
Table Turing machine      10
Tape      7 13
Tape position      8
Tape position, successor      11
Tape, blank      7
Tape, input      11
Tape, output      11
Tape, two-way infinite      13 14
Tarski's Undefinability Theorem      55
Theory of $\mathfrak{N}$       54
Theory of a set of sentences      44
TM      9
Turing computable function      26
Turing computable relation      36
Turing machine      7 9
Turing machine, table      10
Two-way infinite tape      13 14
Unary notation      26
Unbounded minimalization      35
Undefinability Theorem Tarski's      55
Universal Turing machine      17 22 38
UTM      17
Zero function      29

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